Optimal strategy for controlling transport in inertial Brownian motors

TL;DR

This paper investigates optimal control strategies for inertial Brownian motors by identifying conditions that maximize current and efficiency, using numerical simulations and theoretical analysis of diffusion and transport quantifiers.

Contribution

It introduces a method to optimize inertial Brownian motor transport by combining numerical simulations with theoretical expressions for diffusion and efficiency.

Findings

Optimal transport regimes identified using efficiency and Péclet number.

Effective diffusion expressed as a generalized fluctuation theorem.

Comparison of diffusion expressions reveals differences involving hop correlations.

Abstract

In order to optimize the directed motion of an inertial Brownian motor, we identify the operating conditions that both maximize the motor current and minimize its dispersion. Extensive numerical simulation of an inertial rocked ratchet displays that two quantifiers, namely the energetic efficiency and the P\'eclet number (or equivalently the Fano factor), suffice to determine the regimes of optimal transport. The effective diffusion of this rocked inertial Brownian motor can be expressed as a generalized fluctuation theorem of the Green -- Kubo type. Addendum and Erratum The expression for the effective diffusion of an inertial, periodically driven Brownian particle in an asymmetric, periodic potential is compared with the step number diffusion which is extracted from the corresponding coarse grained hopping process specifying the number of covered spatial periods within each temporal period. The two expressions are typically different and involve the correlations between the number of hops.